In this paper we consider a risk model
with two correlated classes of insurance business. Asymptotic
results for the deficit at ruin caused by different classes of
insurance business are obtained. Explicit expression for the deficit
at ruin caused by different classes of insurance business are given
when the original claim size random variables are exponentially
distributed. In addition we also give a brief discussion on the
classical risk model perturbed by the Gamma process.
In this paper, we consider the
compound Markov binomial model proposed by Cossette et al.\,(2003).
The defective renewal equations for the conditional and
unconditional Gerber-Shiu discounted penalty function are obtained.
The asymptotic expressions for the Gerber-Shiu discounted penalty
function are then provided.
In this paper, when the surplus
has negative value, we allow the surplus process to continue. We
consider, in the Markov-modulated risk model, the joint distribution
of the supremum, the infimum and the number of zero of the surplus
process before it leaves zero ultimately.
In this paper, the empirical likelihood
method is extended to partial linear models with fixed designs under
-dependent errors. We show that not the usual empirical
likelihood but the blockwise empirical likelihood works in this
situation, and the blockwise empirical log-likelihood ratio is
asymptotically chi-squared distributed. A simulation study is
reported to show its efficiency.
The ordinary ANOVA has been playing an
important role in testing significant factors in experimental
designs since it was developed. Especially for orthogonal designs,
the ANOVA is almost the unique method of analyzing them. When the
columns of an orthogonal array all are allocated by factors or
interactions and it is impossible to do replicates, however, the
ordinary ANOVA is no more applicable because there are no degrees of
freedom left to estimate the error variance. This paper proposes a
new test method for analyzing the orthogonal designs with only one
replicate using complete orthogonal arrays. It is illustrated with
some examples that the proposed method is practicable when the ANOVA
is invalid. When there are a few empty columns of the orthogonal
array used so that the ANOVA is applicable, the proposed method is
more powerful than the ordinary ANOVA for some parameter
configurations.
The probability of success in a Binomial
model is often viewed as a continuous random variable when
needs to be considered. In this note, we study the
mixed Binomial model with the probability of success having the
Kumaraswamy distribution. Stochastic orders and dependence in this
model are discussed; Further, the new models are employed to fit
some real data sets, and the numerical results reveal that KB models
perform better than Beta-Binomial model in some occasions.
Let and be two linear models with new observations. Through matrix rank
method, we derive the necessary and sufficient conditions for the
best linear unbiased predictor (BLUP) of the new observation under
the model is also BLUP under the model
. As applications, the conditions of equality of the
BLUPs under two mixed linear models are also given.
When we are using the local M-estimator with
variable bandwidth to estimate, the collected data are not
independent samples sometimes, but may be some mixing samples.
Therefore, this paper discusses the strong consistency of
M-estimator with variable bandwidth when the observational data are
-mixing processes, and gives two theorems with some weaker
assumptions.
In this paper, we study the perturbed risk
model with two classes of claims and a threshold dividend strategy.
We assume that the two claim counting processes are, respectively,
Poisson and renewal process with generalized Erlang(2) inter-claim
times. Integro-differential equations and certain boundary
conditions satisfied by the Gerber-Shiu penalty functions are
derived in terms of matrices. Finally, we show that the closed form
for the Gerber-Shiu penalty functions can be expressed by the
Gerber-Shiu penalty functions without dividend payments and the
matrix composed of two linearly independent solutions to the
corresponding homogeneous integro-differential equations.